Coordinate Geometry
Circles, Chord Length
jee_main_2026_april_4_shift_2
Grade 12
Question:
The circle with center (2, -3) and radius 4 intersects the x-axis at points A and B. Find the length of chord AB.
A. 2√3
B. 2√5
C. 2√7
D. 4√3
Step-by-Step Solution
Key Concept: Find distance from center to x-axis, then use chord length formula.
Step 1: Circle: (x-2)^2 + (y+3)^2 = 16. Step 2: Distance from center (2, -3) to x-axis (y=0) is |−3| = 3. Step 3: Chord length = 2√(r^2 - d^2) = 2√(16 - 9) = 2√7.
Correct Answer: C
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